Power measures derived from the sequential query process

We study a basic sequential model for the discovery of winning coalitions in a simple game, well known from its use in defining the Shapley-Shubik power index. We derive in a uniform way a family of measures of collective and individual power in simple games, and show that, as for the Shapley-Shubik index, they extend naturally to measures for TU-games. In particular, the individual measures include all weighted semivalues. We single out the simplest measure in our family for more investigation, as it is new to the literature as far as we know. Although it is very different from the Shapley value, it is closely related in several ways, and is the natural analogue of the Shapley value under a nonstandard, but natural, definition of simple game. We illustrate this new measure by calculating its values on some standard examples.Comment: 13 pages, to appear in Mathematical Social Science

Clinical utility of tibial motor and sensory nerve conduction studies with motor recording from the flexor hallucis brevis: a methodological and reliability study

<p>Abstract</p> <p>Background</p> <p>Standard tibial motor nerve conduction measures are established with recording from the abductor hallucis. This technique is often technically challenging and clinicians have difficulty interpreting the information particularly in the short segment needed to assess focal tibial nerve entrapment at the medial ankle as occurs in posterior tarsal tunnel syndrome. The flexor hallucis brevis (FHB) has been described as an alternative site for recording tibial nerve function in those with posterior tarsal tunnel syndrome. Normative data has not been established for this technique. This pilot study describes the technique in detail. In addition we provide reference values for medial and lateral plantar orthodromic sensory measures and assessed intrarater reliability for all measures.</p> <p>Methods</p> <p>Eighty healthy female participants took part, and 39 returned for serial testing at 4 time points. Mean values ± SD were recorded for nerve conduction measures, and coefficient of variation as well as intraclass correlation coefficients (ICC) were calculated.</p> <p>Results</p> <p>Motor latency, amplitude and velocity values for the FHB were 4.1 ± 0.9 msec, 8.0 ± 3.0 mV and 45.6 ± 3.4 m/s, respectively. Sensory latencies, amplitudes, and velocities, respectively, were 2.8 ± 0.3 msec, 26.7 ± 10.1 μV, and 41.4 ± 3.5 m/s for the medial plantar nerve and 3.2 ± 0.5 msec, 13.3 ± 4.7 μV, and 44.3 ± 4.0 msec for the lateral plantar nerve. All values demonstrated significant ICC values (<it>P </it>≤ 0.007).</p> <p>Conclusion</p> <p>Motor recording from the FHB provides technically clear waveforms that allow for an improved ability to assess tibial nerve function in the short segments used to assess tarsal tunnel syndrome. The reported means will begin to establish normal values for this technique.</p